I have extracted the "support by operating system" section out of the platform support FAQs:

Version by operating system (QuarkXPress 8 to 2018)
If you are planning to use the following operating system, here are the QuarkXPress versions that have been officially supported (or still are) on it:

Using macOS High Sierra (10.13)? QuarkXPress 2016, 2017 & 2018 are supported on this OS.

Planning to use macOS Mojave (10.14)? Please wait until Apple has officially released it and QuarkXPress supports it. QuarkXPress 2018 will support it for sure, not sure yet about QuarkXPress 2017 and 2016. QuarkXPress 2015 will not support Mojave.

NB: Though QX2015 is not officially supported on High Sierra, QX2015 seems to run well on High Sierra with one minor cosmetic issues: Some controls are not shown in Save/Export dialogs. They will appear when you click somewhere (e.g. Desktop shortcut in sidebar).

And – as written in the other post – "not supported" does not necessarily mean "won't work". It just means that Quark didn't test this combination and will also not help you to make this run, it is up to you. If you need technical support by Quark, please use a supported combination has not reached end-of-life.